Try It

Adding and Subtracting Matrices Guided Practices

Practice Problem #1

Given the following matrices:

A equals the 2 by 2 matrix Row-: 1 9 negative 3 Row-: 2 6 5
B equals the 2 by 2 matrix Row-: 1 4 6 Row-: 2 negative 1 7
C equals the 2 by 3 matrix Row-: 1 3 negative 5 4 Row-: 2 negative 2 3 4
D equals the 2 by 3 matrix Row-: 1 negative 5 0 1 Row-: 2 negative 7 1 2

Find the following if it exists: 5A − 3B

5 times the 2 by 2 column matrix Row-: 1 blank blank Row-: 2 blank blank minus 3 times the 2 by 2 matrix Row-: 1 4 6 Row-: 2 negative 1 7
5 times the 2 by 2 matrix Row-: 1 9 negative 3 Row-: 2 6 5 minus 3 times the 2 by 2 matrix Row-: 1 4 6 Row-: 2 negative 1 7

Multiply each matrix by the scalar

A 2 by 2 matrix minus a 2 by 2 matrix with blanks for each element.
the 2 by 2 matrix Row-: 1 45 negative 15 Row-: 2 30 25 minus the 2 by 2 matrix Row-: 1 12 18 Row-: 2 negative 3 21

Subtract the two matrices.

the 2 by 2 column matrix Row-: 1 blank blank Row-: 2 blank blank
the 2 by 2 matrix Row-: 1 33 negative 33 Row-: 2 33 4

Practice Problem #2

Given the following matrices:

A equals the 2 by 2 matrix Row-: 1 9 negative 3 Row-: 2 6 5
B equals the 2 by 2 matrix Row-: 1 4 6 Row-: 2 negative 1 7
C equals the 2 by 3 matrix Row-: 1 3 negative 5 4 Row-: 2 negative 2 3 4
D equals the 2 by 3 matrix Row-: 1 negative 5 0 1 Row-: 2 negative 7 1 2

Find the following if it exists:
C − 3 (D − C)

A 2 by 3 matrix with 3, negative 5, 4 in row 1 and negative 2, 3, 4 in row 2 minus 3 times the difference of the 2 by 3 matrix with negative 5, 0, 1 in row 1 and negative 7, 1, 2 in row 2 and the 2 by 3 matrix with 3, negative 5, 4 in row 1 and negative 2, 3, 4 in row 2.

Subtract the matrices in parentheses

the 2 by 3 matrix Row-: 1 3 negative 5 4 Row-: 2 negative 2 3 4minus three times the 2 by 2 matrix Row-: 1 blank blank Row-: 2 blank blank
the 2 by 3 matrix Row-: 1 3 negative 5 4 Row-: 2 negative 2 3 4 minus 3 times the 2 by 1 column matrix negative 8 negative 5 times the 2 by 1 column matrix 5 negative 2 times the 2 by 1 column matrix negative 3 negative 2

Multiply by the scalar

= the 2 by 3 matrix Row-: 1 3 negative 5 4 Row-: 2 negative 2 3 4 − the 2 by 2 matrix Row-: 1 blank blank Row-: 2 blank blank

= the 2 by 3 matrix Row-: 1 3 negative 5 4 Row-: 2 negative 2 3 4 − the 2 by 3 matrix Row-: 1 negative 24 15 negative 9 Row-: 2 negative 15 negative 6 negative 6

Subtract the two matrices

the 2 by 2 matrix Row-: 1 blank blank Row-: 2 blank blank
the 2 by 3 matrix Row-: 1 negative 27 negative 20 13 Row-: 2 13 9 10